There the game stops. Proof surfaced in 1898 that the reals, complex numbers, quaternions and octonions are the only kinds of numbers that can be added, subtracted, multiplied and divided. The first ...
Quaternions came up while I was interning not too long ago and it seemed like no one really know how they worked. While eventually certain people were tracked down and were able to help with the is...
I'm trying to understand quaternions a bit better and get some more intuition, mostly in the context of using them as a way to think about rotations in 3D. My approach to how one might want to think
I think the geometric algebra interpretation of complex numbers and quaternions is the best, since it reveals more directly the fact that the "imaginary numbers" can be seen as encodings of rotations/reflections.
Introduction to Quaternions_Philip Kelland, Peter Guthrie Tait On Quaternions_William Rowan Hamilton Elements of Quaternions_William Rowan Hamilton Also, to grasp Quaternions intuitively, I recommend this book that I recently found: Visualizing Quaternions by Andrew Hanson. Best of luck in your learning ventures!
linear algebra - Does anyone know any resources for Quaternions for ...
In the quaternion case, reduced means that instead of taking this as the norm, you take its square root. Since the quaternions are 4-dimensional over $\Bbb R$, the reduced norm defines a quadratic form, which is what one would expect from an euclidean norm.
In my application, I make use of quaternions to represent the rotation of the device, and I feel it necessary to include a short description of what quaternions are and why they are suitable to represent rotations.